Thus the LHS nickname is to be considered one-and-the-same-thing as the expression on the RHS, as if macro substitution was to take place.

The primary purpose of this syntax is to provide the means for an expression to directly refer to itself. This is not at all the same convention that Tarski provided where a quoted expression is considered to be the name of the expression so that an expression can refer to its name.

With Tarski's convention the true nature of pathological self-reference cannot be expressed, it slips through the cracks of expressibility without ever being seen.

We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion, Formal_Systems is a predefined constant that is defined to have at least one element.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing as theexpression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression is consideredto be the name of the expression so that an expression can refer to itsname.With Tarski's convention the true nature of pathological self-referencecannot be expressed, it slips through the cracks of expressibilitywithout ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have at leastone element.

So how is "L ∈ Formal_Systems, ∃Γ ⊂ L (Γ ⊢ X)" to be read?"L ∈ Formal_Systems and ∃Γ ⊂ L (Γ ⊢ X)"? I ask because I'm notfamiliar with , in this context.

Also the three formulae with occurrences of ~ in them are meaningless byyour own admission.

--Do, as a concession to my poor wits, Lord Darlington, just explainto me what you really mean.I think I had better not, Duchess. Nowadays to be intelligible isto be found out. -- Oscar Wilde, Lady Windermere's Fan

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing as the expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for an expression to directly refer to itself. This is not at all the same convention that Tarski provided where a quoted expression is considered to be the name of the expression so that an expression can refer to its name.With Tarski's convention the true nature of pathological self-reference cannot be expressed, it slips through the cracks of expressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion, Formal_Systems is a predefined constant that is defined to have at least one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need is

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing as the expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for an expression to directly refer to itself. This is not at all the same convention that Tarski provided where a quoted expression is considered to be the name of the expression so that an expression can refer to its name.With Tarski's convention the true nature of pathological self-reference cannot be expressed, it slips through the cracks of expressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion, Formal_Systems is a predefined constant that is defined to have at least one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

--- G @ ∀L ∈ Formal_Systems, ~∃Γ ⊂ L (Γ ⊢ G)

The above expression named G is enormously simpler than the 1931 Incompleteness Theorem:https://plato.stanford.edu/entries/goedel-incompleteness/

"The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F."

The above expression named G is neither provable nor refutable in any formal system what-so-ever.

If we stopped our analysis right there we would have an enormous simplification of the 1931 GIT that is much broader in scope than the 1931 GIT in that it simultaneously applies to every possible formal system of logic.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?

Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

--Do, as a concession to my poor wits, Lord Darlington, just explainto me what you really mean.I think I had better not, Duchess. Nowadays to be intelligible isto be found out. -- Oscar Wilde, Lady Windermere's Fan

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics". Even if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.

I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code.

Please do just that.What language do you propose to code this computer system in?

It is currently in C++, I am looking for a way to port it to C# so that my $8.00 per month website can directly run the code. I just updated to the most recent version of Bison and Flex.

I was looking into Coco/R and ALTLRCoco/R takes 70 KB versus 108 MB for the same parser. 1600-fold less memory.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code.

Please do just that.What language do you propose to code this computer system in?

It is currently in C++, I am looking for a way to port it to C# so that my $8.00 per month website can directly run the code. I just updated to the most recent version of Bison and Flex.I was looking into Coco/R and ALTLRCoco/R takes 70 KB versus 108 MB for the same parser. 1600-fold less memory.

Post by Pete OlcottMy version has a much broader scope because the 1931 Theorem onlyapplied to Principia Mathematica.

No it doesn't.

--Do, as a concession to my poor wits, Lord Darlington, just explainto me what you really mean.I think I had better not, Duchess. Nowadays to be intelligible isto be found out. -- Oscar Wilde, Lady Windermere's Fan

Post by Pete OlcottMy version has a much broader scope because the 1931 Theorem onlyapplied to Principia Mathematica.

No it doesn't.

I know that such niceties as proving what one claims are of no interestto you, but nevertheless I refer you to Gödel's theorem VI. After allthe many posts of yours about (supposedly) Gödel's incompletenesstheorem you still don't know what it says.

--Do, as a concession to my poor wits, Lord Darlington, just explainto me what you really mean.I think I had better not, Duchess. Nowadays to be intelligible isto be found out. -- Oscar Wilde, Lady Windermere's Fan

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.My version has a much broader scope because the 1931 Theorem only applied to Principia Mathematica.

It is impossible to encode the above semantic meaning in any formal system and either prove or refute the above expression within that formal system.

Many formal systems will not be able to prove or refute the above expression simply because they are not sufficiently expressive to encode its semantic meaning.

Therefore the above expression is neither provable nor refutable within any formal system of the set of all formal system of logic.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.My version has a much broader scope because the 1931 Theorem only applied to Principia Mathematica.

It is impossible to encode the above semantic meaning in any formal system and either prove or refute the above expression within that formal system.Many formal systems will not be able to prove or refute the above expression simply because they are not sufficiently expressive to encode its semantic meaning.Therefore the above expression is neither provable nor refutable within any formal system of the set of all formal system of logic.

Nice,so maybe it's time to fuck off and keep your garbage theories for yourselves somewhere else.A.

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.My version has a much broader scope because the 1931 Theorem only applied to Principia Mathematica.

It is impossible to encode the above semantic meaning in any formal system and either prove or refute the above expression within that formal system.Many formal systems will not be able to prove or refute the above expression simply because they are not sufficiently expressive to encode its semantic meaning.Therefore the above expression is neither provable nor refutable within any formal system of the set of all formal system of logic.

Nice,so maybe it's time to fuck off and keep your garbage theories for yourselves somewhere else.A.

Post by Pete OlcottMany formal systems will not be able to prove or refute the aboveexpression simply because they are not sufficiently expressive toencode its semantic meaning.

If "the above expression simply" means "G @ ∀L ∈ Formal_Systems, ~∃Γ ⊂ L(Γ ⊢ G)", then so what? It is an expression of your devising andtherefore of interest only to you.

Post by Pete OlcottTherefore the above expression is neither provable nor refutablewithin any formal system of the set of all formal system of logic.

--Do, as a concession to my poor wits, Lord Darlington, just explainto me what you really mean.I think I had better not, Duchess. Nowadays to be intelligible isto be found out. -- Oscar Wilde, Lady Windermere's Fan

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.My version has a much broader scope because the 1931 Theorem only applied to Principia Mathematica.

MTT is the universal meta-language that can encode the semantic meaning of every object language (including itself).

https://plato.stanford.edu/entries/tarski-truth/#ObjLanMet

That MTT is a universal meta-language that can even encode its own semantic meaning extends Tarki's ideas significantly. No need for Tarski's infinite hierarchy of languages, the semantic formalization "buck" stops at MTT.

This advance is only made possible because MTT encodes the meanings of its target objects using the smallest possible unit of meaning. Not a Jerry Fodor semantic atom:https://plato.stanford.edu/entries/language-thought/

Post by Pete OlcottThus the LHS nickname is to be considered one-and-the-same-thing asthe expression on the RHS, as if macro substitution was to take place.The primary purpose of this syntax is to provide the means for anexpression to directly refer to itself. This is not at all the sameconvention that Tarski provided where a quoted expression isconsidered to be the name of the expression so that an expression canrefer to its name.With Tarski's convention the true nature of pathologicalself-reference cannot be expressed, it slips through the cracks ofexpressibility without ever being seen.We use: L ∈ Formal_Systemsinstead of: ∃L ∈ Formal_Systemsbecause L ∈ Formal_Systems is an axiom and not an assertion,Formal_Systems is a predefined constant that is defined to have atleast one element.

Why do you introduce Γ? Isn't it true that if Γ ⊢ X then, forany G such that Γ ⊂ G, G ⊢ X? It appears all you need isNot, I fear, very enlightening.

The above expression named G is enormously simpler than the 1931

So is, let's say, 2+3=5. "So what?" people will ask "since 2+3=5 hasnothing to do with GIT." And your G is just the same. If you ever wantto know what GIT says, how it's proved, and what theneither-provable-nor-refutable statement really is, read Mendelson.

Post by Pete Olcotthttps://plato.stanford.edu/entries/goedel-incompleteness/"The first incompleteness theorem states that in any consistent formalsystem F within which a certain amount of arithmetic can be carried out,there are statements of the language of F which can neither be provednor disproved in F."The above expression named G is neither provable nor refutable in anyformal system what-so-ever.If we stopped our analysis right there we would have an enormoussimplification of the 1931 GIT that is much broader in scope than the1931 GIT in that it simultaneously applies to every possible formalsystem of logic.

What are you saying, that you have an incompleteness theorem that isapplicable to every possible formal system of logic? Even those whichare complete?Can you ask yourself whether the readers of sci.lang want to read yourposts? If you think the answer may be "no", perhaps you'd like to stopposting there?

This part of his stuff does not apply to sci.lang but he keepsasserting his theory reflects, or is based on, natural language.

The formalization of the entire set of all semantic meaning equally applies to formal languages and natural languages, thus it is both the formal semantics of linguistics as well as the semantics of logical inference.

But so far you haven't presented even a plausible formal"semantics".

The whole idea of credibility and thus plausibility is complete crap.Credibility is a cheap hooker stand-in for measuring actual validity.

Post by DKleineckeEven if you do it does not follow that youhave said anything meaningful about the semantics ofhuman speech. If anything is clear about this issue it isthat the human mind does not work like a computer.

It would take up more than the rest of my life to sufficiently explain how this applies to natural language to anyone that does not already have Doug Lenat's level of understanding of these things.I will simply create a computer system that can totally understand what I am saying and then people can examine its source code. I just completed the YACC BNF specification for Minimal Type Theory today.My version has a much broader scope because the 1931 Theorem only applied to Principia Mathematica.

MTT is the universal meta-language that can encode the semantic meaning of every object language (including itself).https://plato.stanford.edu/entries/tarski-truth/#ObjLanMetThat MTT is a universal meta-language that can even encode its own semantic meaning extends Tarki's ideas significantly. No need for Tarski's infinite hierarchy of languages, the semantic formalization "buck" stops at MTT.https://plato.stanford.edu/entries/language-thought/{Things} and {Relations} between {Things}.

To describe the above more completely I will have to formulate an axiomatic set theory that is entirely logically coherent. In the mean time one can think of {Things} as the proper class that has everything besides itself as a member and {Relations} as a proper subset of {Things}.

{Things} will contain some elements that are logically incoherent. These will exist within the category of {Misconceptions}.